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*> \brief \b DGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DGESC2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesc2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesc2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesc2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
* .. Scalar Arguments ..
* INTEGER LDA, N
* DOUBLE PRECISION SCALE
* ..
* .. Array Arguments ..
* INTEGER IPIV( * ), JPIV( * )
* DOUBLE PRECISION A( LDA, * ), RHS( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGESC2 solves a system of linear equations
*>
*> A * X = scale* RHS
*>
*> with a general N-by-N matrix A using the LU factorization with
*> complete pivoting computed by DGETC2.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the LU part of the factorization of the n-by-n
*> matrix A computed by DGETC2: A = P * L * U * Q
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1, N).
*> \endverbatim
*>
*> \param[in,out] RHS
*> \verbatim
*> RHS is DOUBLE PRECISION array, dimension (N).
*> On entry, the right hand side vector b.
*> On exit, the solution vector X.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N).
*> The pivot indices; for 1 <= i <= N, row i of the
*> matrix has been interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[in] JPIV
*> \verbatim
*> JPIV is INTEGER array, dimension (N).
*> The pivot indices; for 1 <= j <= N, column j of the
*> matrix has been interchanged with column JPIV(j).
*> \endverbatim
*>
*> \param[out] SCALE
*> \verbatim
*> SCALE is DOUBLE PRECISION
*> On exit, SCALE contains the scale factor. SCALE is chosen
*> 0 <= SCALE <= 1 to prevent overflow in the solution.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleGEauxiliary
*
*> \par Contributors:
* ==================
*>
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
*
* =====================================================================
SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
* -- LAPACK auxiliary routine (version 3.8.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2017
*
* .. Scalar Arguments ..
INTEGER LDA, N
DOUBLE PRECISION SCALE
* ..
* .. Array Arguments ..
INTEGER IPIV( * ), JPIV( * )
DOUBLE PRECISION A( LDA, * ), RHS( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, TWO
PARAMETER ( ONE = 1.0D+0, TWO = 2.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP
* ..
* .. External Subroutines ..
EXTERNAL DLASWP, DSCAL, DLABAD
* ..
* .. External Functions ..
INTEGER IDAMAX
DOUBLE PRECISION DLAMCH
EXTERNAL IDAMAX, DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. Executable Statements ..
*
* Set constant to control overflow
*
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
* Apply permutations IPIV to RHS
*
CALL DLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 )
*
* Solve for L part
*
DO 20 I = 1, N - 1
DO 10 J = I + 1, N
RHS( J ) = RHS( J ) - A( J, I )*RHS( I )
10 CONTINUE
20 CONTINUE
*
* Solve for U part
*
SCALE = ONE
*
* Check for scaling
*
I = IDAMAX( N, RHS, 1 )
IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
TEMP = ( ONE / TWO ) / ABS( RHS( I ) )
CALL DSCAL( N, TEMP, RHS( 1 ), 1 )
SCALE = SCALE*TEMP
END IF
*
DO 40 I = N, 1, -1
TEMP = ONE / A( I, I )
RHS( I ) = RHS( I )*TEMP
DO 30 J = I + 1, N
RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP )
30 CONTINUE
40 CONTINUE
*
* Apply permutations JPIV to the solution (RHS)
*
CALL DLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
RETURN
*
* End of DGESC2
*
END
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